1. Technical Field
The present invention relates to a golf ball and to a mechanical analysis of the golf ball. More particularly, the present invention relates to a golf ball and to an analysis method for simulating physical properties involving deformation of a golf ball by the finite element method using a model run on a computer.
2. Description of the Related Art
The finite element method is known as a computation method capable of analyzing the properties of an object on a computer by sectioning an intricately-shaped object into discrete elements, and by evaluating any physical quantity in each of the elements. An advantage of the finite element method is that when this method is actually used, even if the user does not necessarily have advanced knowledge of the mechanics of materials and elastodynamics, a phenomenon occurring in the object can be understood. Therefore, the finite element method has been widely used to evaluate various types of structures and objects.
In the finite element method, processing is performed at the outset to generate a collection of elements according to the phenomenon or physical quantity to be evaluated or the construction of object. The mode of generating the elements, which is often called mesh sectioning, is known so as to have a great influence on the computation accuracy of the finite element method.
On the other hand, for an object having a three-dimensional shape close to that of a solid sphere, such as a golf ball, the finite element method is used at the design stage to choose a proper material or determine the construction for the purpose of designing a golf ball that achieves both long carry and good controllability (for example, Japanese Unexamined Patent Application Publication No. 2004-13652, and Japanese Unexamined Patent Application Publication No. 2003-288382).
As one ideal element model used for analyzing the mechanical behavior of an object by using the finite element method, a model in which all the elements are formed by small cubes is available. However, it is difficult to analyze the mechanical behavior of a golf ball by using such a model. The reason for this is that since the golf ball has a spherical shape, difficulties are encountered in sectioning the modeled solid sphere into elements while forming all of the elements by cubes. Therefore, various schemes have been devised from the viewpoint of increasing accuracy and computation speed.
FIGS. 1 and 2 show a conventional element setting method used for simulating a golf ball by using the finite element method. FIG. 1 is a computer display image showing a mesh in a cross section of a conventional golf ball model 100 disclosed in Japanese Unexamined Patent Application Publication No. 2004-13652. In this model 100, an outermost layer zone 106 is sectioned in a fine mesh to make computations. Generally, the number of elements is increased by making the mesh finer, and accordingly, the number of nodes increases, so that the computation accuracy in the outermost layer zone 106 increases. For this model, however, the mesh of an inner layer zone 102 is sectioned so that the volume of each element increases toward the outside. Also, in the element in the inner layer zone 102, the aspect ratio is also high. Therefore, in the case of mesh sectioning as in the model 100, there is a high probability that the model behaves as if a central part 102a of the inner layer zone 102 is harder than the physical property value of a real material, and thus it is difficult to say that a uniform physical property value is reproduced in the innermost layer zone on the computer. Also, in the mesh sectioning in the conventional model 100, since the number of sections only in the outermost layer zone 106 is made large, nodes 106a of the outermost layer zone also exist on the edge line of the solid body constituting the inside element. Therefore, there arises a problem in that there is a high probability that an odd state (separation or stress concentration) will occur between the outermost layer zone 106 and the layer on the inside thereof in computation.
FIG. 2 is a sectional view of a model 200 that simulates a golf ball, the model 200 being disclosed in Japanese Unexamined Patent Application Publication No. 2003-288382. This model 200 has a mesh sectioning such that the elements in an inner layer zone 202 are approximately uniform as compared with the conventional model shown in FIG. 1. The mesh of this model is made such that each of the elements in the inner layer zone 202 is a hexahedron, and the number of nodes of each element is eight (refer to FIG. 3). In this model 200, in order to increase the number of nodes to enhance the computation accuracy, the number of elements must be increased. By the increase in computation amount caused by the increase in the number of elements, much time is required for processing. That is to say, the model 200 has a problem in that it is difficult to shorten the processing time while the computation accuracy is maintained or to enhance the computation accuracy while the processing time is maintained. Also, since the element in the inner layer zone 202 is prepared by designating the interior angle of a quadrangular face, as an outer layer zone 204 or an outermost layer zone 206 is approached from the center, the width of element (a spread of each element, in the three-dimensional sense, for a face perpendicular to the radial direction passing through the center) increases (for example, refer to claims 4 and 5 in Japanese Unexamined Patent Application Publication No. 2003-288382). Therefore, the aspect ratio of such a deformed element, that is, the deformation of the shape of the face from a square tends to increase. When the aspect ratio increases, with respect to the lengthwise direction of the element, the accuracy of approximation of a corresponding portion of an actual golf ball made by the element decreases. Therefore, the above-described model 200 has a problem of decreased computation accuracy.